Question 243674

Start with the given system of equations:

{{{system(5x-8y=24,10x-16y=-9)}}}



{{{-2(5x-8y)=-2(24)}}} Multiply the both sides of the first equation by -2.



{{{-10x+16y=-48}}} Distribute and multiply.



So we have the new system of equations:

{{{system(-10x+16y=-48,10x-16y=-9)}}}



Now add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:



{{{(-10x+16y)+(10x-16y)=(-48)+(-9)}}}



{{{(-10x+10x)+(16y+-16y)=-48+-9}}} Group like terms.



{{{0x+0y=-57}}} Combine like terms.



{{{0=-57}}}Simplify.



Since {{{0=-57}}} is <font size="4"><b>never</b></font> true, this means that there are no solutions. 



So the system is inconsistent.